Question

identifying parallel and perpendicular lines. which statement is true regarding the parallel and perpendicular lines in the diagram? o k || n and w ⊥ m o k || n and n ⊥ m o w || n and n ⊥ m o w || n and w ⊥ m

Explanation:

Step1: Recall parallel - perpendicular line properties

Parallel lines never intersect and perpendicular lines intersect at right - angles.

Step2: Analyze the diagram

In the given diagram, lines \(w\) and \(n\) are in the same plane (\(\mathcal{H}\)) and are parallel (\(w\parallel n\)) as they do not intersect. Also, line \(m\) is perpendicular to the plane \(\mathcal{H}\), so it is perpendicular to all lines in the plane \(\mathcal{H}\) that it intersects. Since \(w\) is in the plane \(\mathcal{H}\) and \(m\) intersects the plane \(\mathcal{H}\), \(w\perp m\).

Answer:

\(w\parallel n\) and \(w\perp m\)